Reamur, on this subject, says:—­“Since bees sometimes make mistakes and rectify them, this must be a proof that they possess the power of reason.”

[Illustration:  QUEEN BEE.]

It is known that bees make four different kinds of cells.  There are first the “royal cells” which are exceptional and are of acorn shape.  Then there are the large cells in which the male bees are reared, and in which provisions are stored when the flowers furnish forth of their abundance.  Then there are the little cells which may be called the “cradles of the working bees,” which are also employed as ordinary store-rooms.  These generally occupy about eight-tenth’s of the total surface of the combs in a hive; and finally there are a certain number of what may be called transition cells.  Although these latter are inevitably irregular, the dimensions of the second or third type are so well calculated that when the decimal system was first established, and people were seeking an incontestable standard of measurement, it was the cell of the bee which was proposed first of all by Reamur.  Each one of these cells is an hexagonal tube placed upon a pyramid form, and each honeycomb is formed of two strata of these tubes, base to base, in such a way that the three lozenges which make the pyramid-like base of one cell form at the same time the pyramid-like bases of the three cells on the other side.

[Illustration:  WORKER.] [Illustration:  DRONE.]

In these prismatic tubes the honey is stored away—­and so that the honey shall not trickle out as it would be likely to do if they were built strictly horizontal—­they are tilted up at the outer edge of an angle of four or five degrees.

“Besides the saving in wax,” says Reamur, speaking of this marvellous building, “which is effected by this arrangement of the cells,—­besides the fact that by this plan the comb may be filled without a single gap, there are other advantages in the way of the solidity thus given....  Every possible advantage in the way of the solidity of each cell is brought about by the manner of its construction, and by its place with reference to the rest of the cells in the comb.”

“Students of geometry know,” says Dr. Reid, “that there are only three shapes that can be employed to divide a surface into, uniform spaces, that shall be regular in shape, and without interstices.

[Illustration:  SECTION OF CELLS CONSTRUCTED BY BEES.]

“They are the equilateral triangle, the square, and the regular hexagon, which latter, in the matter of cell construction, is superior to the two first both from the point of view of strength and utility, and it is just this form that the bees have adopted, precisely as though its advantages were familiar to them.

“Furthermore, the bottoms of the cells form three planes meeting at one point, and it has been demonstrated that both in economy of labor and material this system of construction is the best—­again, the angle of the inclination of the planes affects this question of economy:  this problem has been solved by the bees and confirmed by Maclaurin by abstruse mathematical calculations published in the “Transactions of the Royal Society of London."”